Hi MrsJHR,
I understand you are having an issue with one particular reoccurring calendar entry. When you state you are deleting the entry, are you doing it on your iPhone, from your computer, or from icloud.com? I'm not sure what you mean by "it refreshes back to my calendar."
The resource below has some basic troubleshooting steps for iCloud Calendar. The first thing I would suggest is to backup your iPhone, then see if you can delete the entry from www.icloud.com if you haven't already done so. I've highlighted some key information from the article for you below. Click on the link for complete details.
iCloud: Back up your iOS device to iCloud
https://support.apple.com/kb/PH12520?locale=en_US
Get help using iCloud Calendar - Apple Support
https://support.apple.com/en-us/HT203521
If you store and edit your events using your iCloud account instead of a third-party account, like Google or Yahoo, iCloud will automatically update your calendars.
In iOS 7 or later, see which calendar account your events are updating through:
- Open the Calendar app on your device and tap an event to view Event Details.
- Tap the calendar name to see if the event is updating through an iCloud calendar.
If your device uses multiple accounts like iCloud, Google, and Yahoo, make sure your iCloud calendar is the default Calendar account:
- On your device, tap Settings > Mail, Contacts, Calendars > Default Calendar.
- Tap an iCloud calendar to make it your default Calendar account.
- Tap Settings > Mail, Contacts, Calendars.
- Under Calendars, tap Sync. If Sync is set to All Events, set it to a specific timeframe, such as Events 1 Month Back. If it's already set to a specific duration, set it to All Events.
- Tap the Home button.
- Wait several minutes. Open Calendar, tap Calendars, and pull down to refresh.
Take Care,